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Alchen [17]
3 years ago
14

Please help. Find the area of the following shape

Mathematics
1 answer:
lina2011 [118]3 years ago
7 0

Step-by-step explanation:

Area of parallelogram =b×h

= 7×x

= 7x cm²

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1. Prove or give a counterexample for the following statements: a) If ff: AA → BB is an injective function and bb ∈ BB, then |ff
Fantom [35]

Answer:

a) False. A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1

b) True

c) True

d) B = {1}, A = N, f: N ⇒ {1}, f(x) = 1

Step-by-step explanation:

a) lets use A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1. Here f is injective but 2 is an element of b and |f−¹({b})| = 0., not 1. This statement is False.

b) This is True. If  A were finite, then it can only be bijective with another finite set with equal cardinal, therefore, B should be finite (and with equal cardinal). If A were not finite but countable, then there should exist a bijection g: N ⇒ A, where N is the set of natural numbers. Note that f o g : N ⇒ B is a bijection because it is composition of bijections. This, B should be countable. This statement is True.

c) This is true, if f were surjective, then for every element of B there should exist an element a in A such that f(a) = b. This means that  f−¹({b}) has positive cardinal for each element b from B. since f⁻¹(b) ∩ f⁻¹(b') = ∅ for different elements b and b' (because an element of A cant return two different values with f). Therefore, each element of B can be assigned to a subset of A (f⁻¹(b)), with cardinal at least 1, this means that |B| ≤ |A|, and as a consequence, B is finite.

b) This is false, B = {1} is finite, A = N is infinite, however if f: N ⇒ {1}, f(x) = 1 for any natural number x, then f is surjective despite A not being finite.

4 0
3 years ago
You buy 70 of your favorite songs from a Web site that charges ​$0.98 for each song. What is the cost of 70 ​songs? Use mental m
Leya [2.2K]

Answer: If this isn't a trick question it is $68.60

Step-by-step explanation: You just multiply the 98 cents by the 70 songs.

7 0
3 years ago
Read 2 more answers
On their first day of vacation, a family spent $127.92 for meals. The family spent $160.01 for meals the second day. By what amo
ehidna [41]

Answer:

D=32.09

Step-by-step explanation:

160.01-127.92=32.09

5 0
3 years ago
Read 2 more answers
The radius of a size 5 soccer ball is approximately 11.5 cm. How many square inches of synthetic leather does it
kakasveta [241]

Answer:

1661.06 cm²

Step-by-step explanation:

From the question given above, the following data were obtained:

Radius (r) = 11.5 cm

Size of synthetic leather needed =?

To know how many square centimetres of synthetic leather needed to cover the ball, we shall determine the area of the ball. This can be obtained as follow:

Radius (r) = 11.5 cm

Pi (π) = 3.14

Area of ball =?

The shape of a ball is spherical in nature. Thus, we shall apply the formula for calculating the area of a sphere. This is illustrated below:

A = 4πr²

A = 4 × 3.14 × 11.5²

A = 4× 3.14 × 132.25

A = 1661.06 cm²

Thus, 1661.06 cm² of synthetic leather needed to cover the ball.

6 0
2 years ago
Am I correct?<br><br> Which graph represents the line y= 1/5x
lara31 [8.8K]
Yes. Slope = rise over run so you go up one, over five
5 0
3 years ago
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